Affine deformations of quasi-divisible convex cones

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Andrea Seppi, Institut Fourier, Grenoble

In this talk we will study the geometry of affine deformations of discrete subgroups of SL(3,R) that quasi-divide a proper convex cone, that is, subgroups obtained by adding a translation part in R^3. We give a suitable notion of regular domain, generalizing the work of Mess in Minkowski space, and classify the regular domains invariant under the action of such affine deformation. Moreover we show that each such regular domain is uniquely foliated by convex surfaces of constant affine Gaussian curvature, extending a result of Barbot-Béguin-Zeghib. This is joint work with Xin Nie.